AREA AND POLYGONS

Area and polygons :

A polygon is a plane shape with straight sides.The area of a polygon measures the size of the region enclosed by the polygon. It is measured in units squared.

Here you can find area of different polygons.

Area of polygons - Formula

triangle with all three sides of equal length. All the angles are 60°.

Area of equilateral triangle

= (√3/4) a²

scalene triangle is a triangle that has three unequal sides.

Area of scalene triangle

= √s(s-a)(s-b)(s-c)

parallelogram is a quadrilateral with opposite sides parallel.

Area of parallelogram

  = b x h

A shape which is having four sides is generally called quadrilateral. 

Area of quadrilateral

= (1/2) x d x (h₁+h₂)

A plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square.

Area of rectangle

 =  length x breadth

A plane figure with four equal straight sides and four right angles.

Area of square 

  =  4 a 

rhombus is a parallelogram with four equal sides and opposite equal angles.

Area of rhombus

 =  (1/2) x (d₁ x d₂)

A quadrilateral with one pair of sides parallel.

Area of trapezium

 =  (1/2) x h (a+ b)

Area and polygons examples

Example 1 :

Find the area of the parallelogram

Solution :

Area of the parallelogram = b x h

here base (b) = 14 cm and

height (h) = 6 cm

  =  14 x 6

  =  84 cm²

Let us see the next example problem on "Area and polygons"

Example 2 :

What is the area of a parallelogram that has a base of 12 ¾ in  and a height of 2 ½ in.?

Solution :

Area of the parallelogram = b x h

here base (b) = 12 ¾  inches => 51/4 inches

height (h) = ½ => 5/2 inches 

  =  (51/4) x (5/2)

  =  (255/8)

Converting this improper fraction into mixed fraction, we get 31 ⅞ square inches

Let us see the next example problem on "Area and polygons"

Example 3 :

Find the area of trapezoid

Solution :

Area of the trapezoid = (1/2) h (a + b)

a = 36 inches, b = 42 inches and h = 24 inches

  =  (1/2) x 24 (36 + 42)

  =  (1/2) x 24 x 78

  =  936 in²

Example 4 :

The bases of a trapezoid are 11 meters and 14 meters. Its height is 10 meters. What is the area of the trapezoid?

Solution :

Area of the trapezoid = (1/2) h (a + b)

a = 11 m, b = 14 m and h = 10 m

  =  (1/2) x 10 (11 + 14)

  =  5 x 25

  =  125 m²

Example 5 :

The diagonals of a rhombus are 21 m and 32 m. What is the area of the rhombus?

Solution :

Area of rhombus =  (1/2) x (d₁ x d₂)

d₁ = 21 m and d₂ = 32 m

  =  (1/2) x (21 x 32)

  =  21 x 16

  =  336 m²

Example 6 :

Find the area of the given figure. Explain how you found your answer.

Solution :

In the given figure we can find two shapes trapezium and rectangle.

ABCD  is a trapezium

DCEF is a rectangle

Area of the given figure

 =  area of trapezium + area of rectangle

Area of trapezium (ABCD) = (1/2) x h (a+ b)

DC = EF = 18 ft

a = 10 ft, b = 18ft and h = 6 ft

  =  (1/2) x 6 x (10 + 18) ==> 84 square ft

Area of rectangle (DCEF) = length x breadth

length = 18 ft and breadth = 12 ft

  =  18 x 12 ==> 216 square ft

Area of given figure  =  84 + 216  

=  300 square ft 

Related topics

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